While it's true any sword sharpened on one side and not on the other could be called "monoedged", in this case what is being implied is a blade with an edge that is one molocule thick and incredibly sharp. The blade does of course get dulled with use, but the scabbard it is kept in resharpens it with every unsheathing.
Melee: Attacks with this trait can be used during close combat without penalty.
Penetrating: When a weapon with this trait successfully hits, it has D3 Armor Penetration against the target.
Parry: After an enemy makes close combat attacks against this fighter and rolls to hit, until this fighter has no further Parry options available to them this fighter's controlling player can force the attacking player to re-roll one successful hit per Parry.